Gauge theory and nematic order : the rich landscape of orientational phase transition

As crystals are classified by space groups, nematic liquid crystals should be in principle classified by point groups. Conventionally, the study of nematic liquid crystals has mainly been focused on a very small subset of the whole nematic family, partly because of limitations of traditional methods. In this thesis, we introduce a non-Abelian gauge theory that can treat nematic phases with arbitrary point group symmetries in a unified framework in an efficient way. The proposed gauge theory allows us to compare nematic phases against a common reference. We are therefore able to quantify the orientational fluctuations of nematic orders with different symmetries and identify a novel chiral liquid phase. Moreover, this gauge theory can act as an order-parameter generator, and we thus achieve a full classification of nematic-order-parameter tensors, which has never been done before. Finally, we show that the gauge theory provides a convenient way to access the anisotropy of axial orders, by which we generalize the extensively studied biaxial-uniaxial transition of D2h nematics to a much broader class.